基于有限域欧几里德算法的RS码识别

Recognition Method of RS Codes Based on Euclidean Algorithm in Galois Field

针对基于有限域傅里叶变换的RS码识别方法存在复杂度高、计算量大的不足,提出了基于有限域欧几里德算法的RS码识别方法。该方法利用有限域欧几里德算法计算RS码与其循环移位码字间的最大公约式,通过遍历码长时得到的最大公约式指数的最大值与平均值的最大差来识别码长,根据识别的码长所对应的最大公约式指数的最大值识别本原多项式,进而对最大公约式进行因式分解识别生成多项式。理论分析和仿真实验表明:本识别算法较现有方法减少了数十倍的计算量,在误码率为10-3的情况下,对RS码的识别概率高于90%。

The recognition method of RS Codes based on Galois Field Fourier Transform （GFFT） is of much complexity and computation amount. Aiming at the problems, a recognition method of RS Codes based on Euclidean algorithm in Galois Field was proposed in this paper. The greatest common divisor （GCD） between RS codeword and its circular shift codeword was computed by Euclidean algorithm in Galois Field, then the code length of RS codes was estimated by use of the maximum difference between the maximum and mean value of the GCD index （obtained by searching all the possible code length）. The primitive polynomial was recognized according to the obtained code length which corresponded with the maximum value of the GCD index. Finally, the creating polynomial was gained by factorizing the GCD. The academic analysis and simulation experiments showed that the computing time of foregone method was ten times as high as this method,and it had a 90% recognition probability at an error code rate of 1 × 10^-3.